Question: Simplify the following expression: $\dfrac{90p^4}{10p}$ You can assume $p \neq 0$.
Explanation: $ \dfrac{90p^4}{10p} = \dfrac{90}{10} \cdot \dfrac{p^4}{p} $ To simplify $\frac{90}{10}$ , find the greatest common factor (GCD) of $90$ and $10$ $90 = 2 \cdot 3 \cdot 3 \cdot 5$ $10 = 2 \cdot 5$ $ \mbox{GCD}(90, 10) = 2 \cdot 5 = 10 $ $ \dfrac{90}{10} \cdot \dfrac{p^4}{p} = \dfrac{10 \cdot 9}{10 \cdot 1} \cdot \dfrac{p^4}{p} $ $\phantom{ \dfrac{90}{10} \cdot \dfrac{4}{1}} = 9 \cdot \dfrac{p^4}{p} $ $ \dfrac{p^4}{p} = \dfrac{p \cdot p \cdot p \cdot p}{p} = p^3 $ $ 9 \cdot p^3 = 9p^3 $